{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "fc5c026e-bdd4-4f2f-8c63-987ca2930009",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X = np.array([-3,-2,-1,1,2,3])\n",
    "y = np.array([1, 0, 0, 1, 1, 0])\n",
    "\n",
    "def sigmoid(x, w, b):    \n",
    "    return 1/(1 + np.exp(b + w*x))\n",
    "\n",
    "def celoss(w, b):\n",
    "    n = y.shape[0]\n",
    "    s = 0.0\n",
    "    \n",
    "    for i in range(n):\n",
    "        y_hat = sigmoid(X[i], w, b)\n",
    "        s += y[i]*np.log(y_hat) + (1 - y[i])*np.log(1 - y_hat)\n",
    "    \n",
    "    return -s/n\n",
    "\n",
    "def loss2(w, b):\n",
    "    n = y.shape[0]\n",
    "    s = 0.0\n",
    "    for i in range(n):\n",
    "        s += (y[i] - sigmoid(X[i], w, b))**2\n",
    "    \n",
    "    return s\n",
    "\n",
    "w_min = -5\n",
    "w_max = 5\n",
    "b_min = -10\n",
    "b_max = 10\n",
    "\n",
    "w_range = np.arange(w_min, w_max, 0.05)\n",
    "b_range = np.arange(b_min, b_max, 0.05)\n",
    "\n",
    "w_grid, b_grid = np.meshgrid(w_range, b_range)\n",
    "\n",
    "def plt_grid(loss_grid,path):\n",
    "    fig = plt.figure()\n",
    "    ax = plt.axes(projection='3d')\n",
    "\n",
    "    #ax.plot_wireframe(t1_arr, t2_arr, cost_arr,  color='black')\n",
    "    ax.plot_surface(w_grid, b_grid, loss_grid, cmap='Blues_r', antialiased=False, edgecolor='none', vmin =np.min(loss_grid), vmax =2*np.max(loss_grid))\n",
    "    ax.set_xlabel(r'$w$', fontsize=20)\n",
    "    ax.set_ylabel(r'$b$', fontsize=20)\n",
    "    ax.set_zlabel(r'$C(\\theta)$', fontsize=20)  \n",
    "    ax.view_init(25, -120)\n",
    "    fig.savefig(path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "6b21b22d-ab49-431d-962d-8a10ba48f22f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_grid(loss2(w_grid, b_grid),\"/Users/uqjnazar/Dropbox/MathEngDeepLearningBook/LaTeXBook/figures/chapter_3_figures/Logit_SE_Loss.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b6009952-e3da-4aae-8b52-a3ab62bbf408",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_grid(celoss(w_grid, b_grid),\"/Users/uqjnazar/Dropbox/MathEngDeepLearningBook/LaTeXBook/figures/chapter_3_figures/Logit_CE_Loss.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "805142d1-306a-4697-9e86-9b1f2d399745",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
